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On Poisson brackets of hydrodynamic type with degenerate metric. (Russian) Zbl 0611.58017

It is established that for reducing the metric tensor \((g^{ij})\) with degeneration of the constant rank m, rank \(g^{ij}=m\leq n\), to the form \(g^{ij}\equiv const\) by local transformations it is necessary for the system in question to be the Poisson brackets. The cases \(m=n-1\), n-2 and other examples are considered in detail.
Reviewer: G.Il’jusina

MSC:

53D17 Poisson manifolds; Poisson groupoids and algebroids
37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
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